Psychic is good STAB and hits Poison-types.
Thunderbolt is good for hitting Waters and and Flyers also is a good move overall.
Shadow Ball hits Ghosts and Psychics.
Scarfed Destiny Bond can give something a Nasty Surprise.

Special ATtacker
Psychic: Good power, high accuracy, chance to lower Sp. Def, STAB.
Shadow Ball: Good power, high accuracy, decent chance to lower Sp. Def, deals with Ghost and other Psychic types.
Focus Blast: High power, chance to lower Sp. Def, deals with Dark and Steel types.
Will-o-wisp: Burns the foe, which damages and lowers Attack.

Special Attacker 2
Psychic: Good power, high accuracy, chance to lower Sp. Def, STAB.
Calm Mind: Increases special stats.
Thunderbolt: Good power, high accuracy, chance to paralyze.
Will-o-wisp: Burns the foe, which damages and lowers Attack.

Helper
Healing Wish: For when you have used all your other moves.
Toxic: Inflicts bad poison.
Light Screen: Raises the Sp. Def of your team.
Reflect: Raises the Def of your team.

Staller
Encore: To trap the foe in a move that isn't good.
Hypnosis: Puts the foe to Sleep and allows for Dream Eater.
Dream Eater: Used with Hypnosis. High power, high accuracy, STAB, heals Gardevoir.
Attract: Infatuates the foe.

Last Ditch Effort
Psychic: Good power, high accuracy, chance to lower Sp. Def, STAB.
Thunderbolt: Good power, high accuracy, chance to paralyze.
Calm Mind: Increases special stats.
Destiny Bond: Used as a way to take the foe down with you.

Last Ditch Effort 2
Psychic: Good power, high accuracy, chance to lower Sp. Def, STAB.
Calm Mind: Raises special stats.
Destiny Bond: A way to take the foe down with you.
Thunder Wave: Paralyzes the foe.

Ally Switch/Telekinesis -ally switch lets gardivoir take a hit for a teammate(which with these ev's, it should be able to take the hit) and gives them a wish, it could also be very confusing for your opponent, or telekinesis makes the opponent easier to hit

Psychic -your not total taunt bait

252 Defense - helps with that subpar defense

126 SpDefense - boosts that already stelar SpDef

126 Speed - makes sure that you can go to work before something bad happens

First, use Mean Look. The opponent won't be able to escape anymore. Use Encore then the next turn, if you manage to survive, use Torment or Disable. The foe will now use Struggle and will not be able to escape. You have managed yourself an automatic KO! In the third moveslot, Torment is recommended because Disable doesn't hit Ghosties. Psychic is there so you are not a Taunt bait.

That new retyping of Gardevoir to Psychic/Fairy is fantastic, now it is no longer Pursuit weak and is immune to Dragon-type attacks. Its Mega-Evolution is also excellent, so it is now much more powerful than Life Orb Gardevoir!

Strategy is simple here. Come in on something that Gardevoir can force out, which is actually made easier by Normal Gardevoir's fantastic Trace ability, like switching into a Vaporeon and tracing its Water Absorb, thus forcing it out as it cant do much. Set up with Calm Mind while going mega as they switch, then proceed to sweep.

Shadow Ball + Focus Blast gives perfect neutral coverage, hitting pesky ghosts and steel types for super effective damage (Scizor is a thing but every Pokemon has their counters, no?). Hyper Voice is just insanely powerful, being boosted by STAB and given a 1.3x Boost due to Pixilate. It goes through substitutes, it wrecks souls, just wow. Gardevoir had always been my favorite Pokemon, and it looks like I'm going to love her more than ever before.

As for people asking how does Gardevoir learn Hyper Voice, it learns it by move tutor at the Battle Resort in Pokemon Omega Ruby and Alpha Sapphire.

pixalate changes the whole ball game ! pixilate makes hyper beam fairy! 150 stab = 300 x 1.5 if a critical hit = 450 x 2 if its used against a dragon dark fighting or bug type making it come out to a grand total of 900 damage not counting evs and ivs or amie boosts

so its still 675 and even if its 1/2 power as a critical hit its 225/2 = 112.5 then its still stab = 112.5 x 1.5 = 168.75
if 1/4 then 37.5 times 3 = 112.5 still puts a huge dent but seriously what steel/poison, poison fire , or fire steel are there !

Hyper Beam (Normal-type when Gardevoire, Fairy + Stab in Mega form. The move is a whopping 150 compared to Moonblast's 95 Power, will usually be the difference between a 2HKO and a 1HKO. Horrible re-charge time though, use sparingly on revenge kills and towards the end, and possibly for shock and awe.)

Focus Blast (Attacking Focus Blast to cover steel weakness.)

This Gardevoire is true to it's elegant beauty; it can use five unique move types: Normal, Fairy, Psychic, Ghost, and Fighting. It's weaknesses of poison, steel, and ghost are defeated through both speed and a swift blast of telekinetic awesomeness.

No, HelloPeople. Return and Frustration are both physical moves. Gardevoir's physical attack is terrible compared to its special attack. The difference between Return and Frustration is how much friendship your pokemon has.

Gardevoir deserves any trainers full attention. She can be really or pathetically weak, depending on how she's treated. Here is the EV spread, IV's and stats and moveset I give ALL of my Gardevoirs when I play.

moveset:
Psychic/Psyshock: Depends on if you want to kill all physical defenders, or take down some special walls with bad def. like Snorlax.
Thunderbolt: Great power, good for water and flying types.
Energy Ball/Shadow Ball: Depends on whether you are wanting to take down Ghosts or mudfish like Swampert, which can get annoying.
Signal Beam/Focus Blast/Icy Wind: Yeah, I know. No Calm Mind. I think if her special attack is high enough, why raise it? Besides, Signal Beam is great against Grass, Psychic, and the dreaded Dark type. Focus Blast is also good for Darks, but is pretty inaccurate. I'd rather go with Icy Wind. But its your choice.